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Step-by-step practice: Maths · Level 5Chapter 2 · Adding and subtracting whole numbers to a million
Level 5 · Chapter 2

Adding and subtracting whole numbers to a million

By the end of this chapter you will be able to

  • Add two numbers to 999,999 in columns, carrying across several places
  • Subtract in columns, exchanging across zeros
  • Estimate by rounding, and check a sum or difference
  • Find a missing number in a sum or difference
  • Solve two-step problems with numbers to a million

You should already know

  • Column addition and subtraction to 10,000 (Level 4, chapter 3)
  • Place value to a million (chapter 1)

Where this leads

  • Long multiplication (chapter 4)
  • Fractions with the same denominator (chapter 6)

Step-by-step practice: maths (Level 5). Small steps, repeated until fluent. Content: Add and subtract whole numbers with more than four digits, using columnar methods (Y5 paraphrase), Use rounding to check answers and estimate, and decide the level of accuracy (Y5 paraphrase), Solve addition and subtraction multi-step problems (Y5 paraphrase), Solve missing number problems (Y5 paraphrase).

Exercise P  Do you remember?

Non-calculator
1
FWork out 4,375 + 2,819.
2
FWork out 6,048 + 1,965.
3
FWork out 5,000 - 2,346.
4
FWhat is 7 × 8?
5
FWhat is 30,000 more than 245,000?
2.1

Adding in columns with carrying

Level 5
Add two numbers with up to six digits, in columns
Video lesson: Adding in columns with carryingComing soon

Line up the digits in columns, so that ones are under ones and thousands are under thousands. Start from the right.

When a column adds up to ten or more, write the ones digit and carry the ten to the next column on the left.

Key ideas

  • Line up the columns, with the ones on the right.
  • Add one column at a time, starting from the right.
  • Carry a ten into the next column on the left.
Worked example 2.1.1
Work out 265,384 + 48,973.

Method. Add the columns from the right. Carry any ten into the next column on the left.

  1. Add the ones column. Write 7 in the ones column.
    4 + 3 = 7
  2. Add the tens column. Write 5 and carry 1 to the hundreds column.
    8 + 7 = 15
  3. Add the hundreds column. Write 3 and carry 1 to the thousands column.
    3 + 9 + 1 carried = 13
  4. Add the thousands column. Write 4 and carry 1 to the ten thousands column.
    5 + 8 + 1 carried = 14
  5. Add the ten thousands column. Write 1 and carry 1 to the hundred thousands column.
    6 + 4 + 1 carried = 11
  6. Add the hundred thousands column. Write 3 in the hundred thousands column.
    2 + 0 + 1 carried = 3
  7. Write the answer. Put the digits together, with commas between groups of three.
    314,357

Check. Check: 314,357 - 48,973 = 265,384.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Worked example 2.1.2
Work out 698,765 + 301,247.

Method. Add the columns from the right. Carry any ten into the next column on the left.

  1. Add the ones column. Write 2 and carry 1 to the tens column.
    5 + 7 = 12
  2. Add the tens column. Write 1 and carry 1 to the hundreds column.
    6 + 4 + 1 carried = 11
  3. Add the hundreds column. Write 0 and carry 1 to the thousands column.
    7 + 2 + 1 carried = 10
  4. Add the thousands column. Write 0 and carry 1 to the ten thousands column.
    8 + 1 + 1 carried = 10
  5. Add the ten thousands column. Write 0 and carry 1 to the hundred thousands column.
    9 + 0 + 1 carried = 10
  6. Add the hundred thousands column. Write 0 and carry 1 to the millions column.
    6 + 3 + 1 carried = 10
  7. Write the last carried 1. It goes in front of the other digits.
    1 in the millions column
  8. Write the answer. Put the digits together, with commas between groups of three.
    1,000,012

Check. Check: 1,000,012 - 301,247 = 698,765.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Worked example 2.1.3
Work out 38,456 + 27,967.

Method. Add the columns from the right. Carry any ten into the next column on the left.

  1. Add the ones column. Write 3 and carry 1 to the tens column.
    6 + 7 = 13
  2. Add the tens column. Write 2 and carry 1 to the hundreds column.
    5 + 6 + 1 carried = 12
  3. Add the hundreds column. Write 4 and carry 1 to the thousands column.
    4 + 9 + 1 carried = 14
  4. Add the thousands column. Write 6 and carry 1 to the ten thousands column.
    8 + 7 + 1 carried = 16
  5. Add the ten thousands column. Write 6 in the ten thousands column.
    3 + 2 + 1 carried = 6
  6. Write the answer. Put the digits together, with commas between groups of three.
    66,423

Check. Check: 66,423 - 27,967 = 38,456.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Watch out

Watch out. Carried tens go into the next column, not the one under it. Add the carried number first.

Exam tip

Grown-up tip. Ask the child to say the carry aloud: “Seven and five is twelve, write two and carry one.”

Exercise 2A  Practice: adding in columns

Non-calculator
1
FWork out 272,681 + 568,137.
2
FWork out 529,999 + 151,562.
3
FWork out 381,275 + 188,498.
4
FWork out 128,212 + 796,556.
5
FWork out 836,726 + 129,251.
6
FWork out 888,575 + 47,036.
7
FWork out 854,298 + 105,170.
8
FWork out 377,681 + 275,781.
9
FWork out 136,517 + 414,684.
10
FWork out 60,699 + 317,881.
11
FWork out 240,936 + 236,246.
12
FWork out 342,650 + 466,437.
13
FWork out 875,376 + 118,304.
14
FWork out 509,991 + 155,279.
15
FWork out 247,646 + 420,053.
16
FWork out 515,342 + 215,022.
2.2

Carrying across several places

Level 5
Add numbers that need carrying in several columns, and check the answer
Video lesson: Carrying across several placesComing soon

Some sums carry in every column. Each carried 1 is added to the next column, so it can make another ten.

Check by subtracting one of the numbers from the total. You should get the other number back.

Key ideas

  • Carries can happen in several columns in one sum.
  • Add the carried 1 before you add the next pair of digits.
  • Check the total by taking away one of the numbers.
Worked example 2.2.1
Work out 286,549 + 567,892.

Method. Add the columns from the right. Carry any ten into the next column on the left.

  1. Add the ones column. Write 1 and carry 1 to the tens column.
    9 + 2 = 11
  2. Add the tens column. Write 4 and carry 1 to the hundreds column.
    4 + 9 + 1 carried = 14
  3. Add the hundreds column. Write 4 and carry 1 to the thousands column.
    5 + 8 + 1 carried = 14
  4. Add the thousands column. Write 4 and carry 1 to the ten thousands column.
    6 + 7 + 1 carried = 14
  5. Add the ten thousands column. Write 5 and carry 1 to the hundred thousands column.
    8 + 6 + 1 carried = 15
  6. Add the hundred thousands column. Write 8 in the hundred thousands column.
    2 + 5 + 1 carried = 8
  7. Write the answer. Put the digits together, with commas between groups of three.
    854,441

Check. Check: 854,441 - 567,892 = 286,549.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Worked example 2.2.2
Is 700,001 the correct answer to 582,463 + 117,538? Check it and answer Yes or No.

Method. Check by using the inverse: subtract for a sum, or add back for a difference.

  1. Take one number away from the answer. If the sum is correct, taking one number away gives the other.
    700,001 - 582,463 = 117,538
  2. Compare with the other number. Is 117,538 the same as 117,538?
    Same
  3. Write Yes or No. Yes if the check works; No if it does not.
    Yes

Check. The correct answer is 700,001.

Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.

Worked example 2.2.3
Work out 698,765 + 301,247.

Method. Add the columns from the right. Carry any ten into the next column on the left.

  1. Add the ones column. Write 2 and carry 1 to the tens column.
    5 + 7 = 12
  2. Add the tens column. Write 1 and carry 1 to the hundreds column.
    6 + 4 + 1 carried = 11
  3. Add the hundreds column. Write 0 and carry 1 to the thousands column.
    7 + 2 + 1 carried = 10
  4. Add the thousands column. Write 0 and carry 1 to the ten thousands column.
    8 + 1 + 1 carried = 10
  5. Add the ten thousands column. Write 0 and carry 1 to the hundred thousands column.
    9 + 0 + 1 carried = 10
  6. Add the hundred thousands column. Write 0 and carry 1 to the millions column.
    6 + 3 + 1 carried = 10
  7. Write the last carried 1. It goes in front of the other digits.
    1 in the millions column
  8. Write the answer. Put the digits together, with commas between groups of three.
    1,000,012

Check. Check: 1,000,012 - 301,247 = 698,765.

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.

Watch out

Watch out. A total of 1,000,000 or more has seven digits. Make sure the answer has the right number of digits.

Exam tip

Grown-up tip. Ask the child to check every big sum by subtracting one number from the total.

Exercise 2B  Practice: carrying across several places

Non-calculator
1
FWork out 402,976 + 260,737.
2
FWork out 802,715 + 85,805.
3
FWork out 50,428 + 280,669.
4
FWork out 876,169 + 119,726.
5
FWork out 767,463 + 74,477.
6
FWork out 116,658 + 326,922.
7
FWork out 533,724 + 28,462.
8
FWork out 239,526 + 440,523.
9
FWork out 268,727 + 300,643.
10
FWork out 604,471 + 19,835.
11
FWork out 552,602 + 339,633.
12
FWork out 536,689 + 381,308.
13
FWork out 336,516 + 510,797.
14
FWork out 805,659 + 130,185.
15
FWork out 534,947 + 382,261.
16
FWork out 723,508 + 28,403.
2.3

Subtracting in columns, with exchange

Level 5
Subtract numbers with up to six digits in columns, exchanging across zeros
Video lesson: Subtracting in columns, with exchangeComing soon

When the digit on top is smaller than the digit below, exchange 1 from the column on the left. That 1 is worth 10 in the column you are working in.

If the column on the left is 0, exchange across it. Each zero becomes a 9 as you pass it, and the next digit that is not zero gives 1.

Key ideas

  • Exchange when the top digit is smaller.
  • Exchange across zeros: a zero becomes 9 as you pass it.
  • Work from the right, one column at a time.
Worked example 2.3.1
Work out 500,000 - 273,468.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

  1. Subtract the ones column. 0 is less than 8. The tens and hundreds and thousands and ten thousands are 0, so exchange across them: take 1 hundred thousands and make each zero a 9, which gives 10 ones.
    10 - 8 = 2
  2. Subtract the tens column. 9 is at least 6, so subtract directly.
    9 - 6 = 3
  3. Subtract the hundreds column. 9 is at least 4, so subtract directly.
    9 - 4 = 5
  4. Subtract the thousands column. 9 is at least 3, so subtract directly.
    9 - 3 = 6
  5. Subtract the ten thousands column. 9 is at least 7, so subtract directly.
    9 - 7 = 2
  6. Subtract the hundred thousands column. 4 is at least 2, so subtract directly.
    4 - 2 = 2
  7. Write the answer. Read the digits from the left, and put commas in.
    226,532

Check. Check: 273,468 + 226,532 = 500,000.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Worked example 2.3.2
Work out 400,705 - 98,236.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

  1. Subtract the ones column. 5 is less than 6. The tens is 0, so exchange across them: take 1 hundreds and make each zero a 9, which gives 10 ones.
    15 - 6 = 9
  2. Subtract the tens column. 9 is at least 3, so subtract directly.
    9 - 3 = 6
  3. Subtract the hundreds column. 6 is at least 2, so subtract directly.
    6 - 2 = 4
  4. Subtract the thousands column. 0 is less than 8. The ten thousands is 0, so exchange across them: take 1 hundred thousands and make each zero a 9, which gives 10 thousands.
    10 - 8 = 2
  5. Subtract the ten thousands column. 9 is at least 9, so subtract directly.
    9 - 9 = 0
  6. Subtract the hundred thousands column. 3 is at least 0, so subtract directly.
    3 - 0 = 3
  7. Write the answer. Read the digits from the left, and put commas in.
    302,469

Check. Check: 98,236 + 302,469 = 400,705.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Worked example 2.3.3
Work out 702,530 - 418,096.

Method. Subtract each column from the right. Exchange 1 from the column on the left when the top digit is too small.

  1. Subtract the ones column. 0 is less than 6, so exchange 1 tens for 10 ones.
    10 - 6 = 4
  2. Subtract the tens column. 2 is less than 9, so exchange 1 hundreds for 10 tens.
    12 - 9 = 3
  3. Subtract the hundreds column. 4 is at least 0, so subtract directly.
    4 - 0 = 4
  4. Subtract the thousands column. 2 is less than 8. The ten thousands is 0, so exchange across them: take 1 hundred thousands and make each zero a 9, which gives 10 thousands.
    12 - 8 = 4
  5. Subtract the ten thousands column. 9 is at least 1, so subtract directly.
    9 - 1 = 8
  6. Subtract the hundred thousands column. 6 is at least 4, so subtract directly.
    6 - 4 = 2
  7. Write the answer. Read the digits from the left, and put commas in.
    284,434

Check. Check: 418,096 + 284,434 = 702,530.

Watch out. When you exchange across zeros, change each zero to 9 as you pass it. Do not leave a zero in the middle.

Watch out

Watch out. In 500,000 - 273,468 the top number has zeros in the middle. Every zero must be exchanged across, one column at a time.

Exam tip

Grown-up tip. Ask: “Is the top digit smaller? Which column do you exchange from?” before the child starts to take away.

Exercise 2C  Practice: subtracting with exchange

Non-calculator
1
FWork out 619,229 - 140,289.
2
FWork out 404,137 - 356,718.
3
FWork out 786,045 - 597,586.
4
FWork out 643,231 - 139,818.
5
FWork out 477,306 - 380,326.
6
FWork out 949,527 - 52,283.
7
FWork out 799,573 - 657,611.
8
FWork out 458,079 - 65,464.
9
FWork out 730,297 - 72,974.
10
FWork out 273,819 - 165,276.
11
FWork out 615,574 - 516,073.
12
FWork out 686,447 - 268,860.
13
FWork out 746,841 - 646,832.
14
FWork out 855,943 - 459,256.
15
FWork out 956,170 - 742,688.
16
FWork out 545,521 - 499,929.
2.4

Estimating and checking

Level 5
Estimate by rounding each number first, Check a sum by subtraction and a difference by addition
Video lesson: Estimating and checkingComing soon

An estimate tells you roughly how big the answer should be. Round each number first, then calculate with the rounded numbers.

To check a sum, subtract one number from the total. To check a difference, add the number you took away back on.

Key ideas

  • Round first, then calculate, to estimate.
  • The exact answer should be close to the estimate.
  • Check a sum by subtraction; check a difference by addition.
Worked example 2.4.1
Estimate 482,000 + 310,000 by rounding each number to the nearest 10,000.

Method. Round each number first, then calculate with the rounded numbers.

  1. Round the first number. Look at the thousands digit: 5 or more rounds up.
    482,000 is about 480,000
  2. Round the second number. Use the same rule.
    310,000 is about 310,000
  3. Add the rounded numbers. This is the estimate.
    480,000 + 310,000 = 790,000
  4. Write the estimate. The exact answer should be close to this.
    790,000

Check. The exact answer is 792,000, which is close to 790,000.

Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.

Worked example 2.4.2
Is 700,001 the correct answer to 582,463 + 117,538? Check it and answer Yes or No.

Method. Check by using the inverse: subtract for a sum, or add back for a difference.

  1. Take one number away from the answer. If the sum is correct, taking one number away gives the other.
    700,001 - 582,463 = 117,538
  2. Compare with the other number. Is 117,538 the same as 117,538?
    Same
  3. Write Yes or No. Yes if the check works; No if it does not.
    Yes

Check. The correct answer is 700,001.

Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.

Worked example 2.4.3
Estimate 738,000 - 205,000 by rounding each number to the nearest 10,000.

Method. Round each number first, then calculate with the rounded numbers.

  1. Round the first number. Look at the thousands digit: 5 or more rounds up.
    738,000 is about 740,000
  2. Round the second number. Use the same rule.
    205,000 is about 210,000
  3. Subtract the rounded numbers. This is the estimate.
    740,000 - 210,000 = 530,000
  4. Write the estimate. The exact answer should be close to this.
    530,000

Check. The exact answer is 533,000, which is close to 530,000.

Watch out. Estimate with the rounded numbers, then work out the exact answer with the column method.

Watch out

Watch out. An estimate is not the exact answer. Use the estimate to check that your answer is about the right size.

Exam tip

Grown-up tip. Ask the child: “Is the answer about the right size?” before they check it exactly.

Exercise 2D  Practice: estimating and checking

Non-calculator
1
RIs 688,072 the correct answer to 569,853 + 118,219? Check it and answer Yes or No.
2
FEstimate 236,844 + 314,998 by rounding each number to the nearest 10,000.
3
RIs 994,651 the correct answer to 854,966 + 139,685? Check it and answer Yes or No.
4
RIs 946,272 the correct answer to 869,345 + 75,927? Check it and answer Yes or No.
5
FEstimate 448,428 + 326,766 by rounding each number to the nearest 10,000.
6
FEstimate 459,919 + 25,866 by rounding each number to the nearest 10,000.
7
RIs 304,704 the correct answer to 228,141 + 76,573? Check it and answer Yes or No.
8
RIs 715,368 the correct answer to 303,532 + 401,836? Check it and answer Yes or No.
9
RIs 930,992 the correct answer to 834,723 + 106,269? Check it and answer Yes or No.
10
RIs 926,248 the correct answer to 781,794 + 134,454? Check it and answer Yes or No.
11
RIs 869,153 the correct answer to 266,137 + 603,016? Check it and answer Yes or No.
12
RIs 581,188 the correct answer to 135,649 + 455,539? Check it and answer Yes or No.
13
RIs 867,377 the correct answer to 345,902 + 521,475? Check it and answer Yes or No.
14
RIs 740,005 the correct answer to 191,459 + 548,546? Check it and answer Yes or No.
15
FEstimate 392,244 - 37,060 by rounding each number to the nearest 10,000.
16
FEstimate 363,966 + 191,116 by rounding each number to the nearest 10,000.
2.5

Missing numbers and two-step problems

Level 5
Find a missing number in an addition or subtraction, Solve two-step problems with numbers to a million
Video lesson: Missing numbers and two-step problemsComing soon

To find a missing number in a sum, subtract the known number from the total. To find a missing number in a difference, add.

In a two-step problem, work out the first step, then use the answer to work out the second step.

Key ideas

  • Subtract to find a missing addend.
  • Add to find a missing number in a difference.
  • Do one step at a time, and check the answer fits the story.
Worked example 2.5.1
248,000 + ___ = 300,000. What is the missing number?

Method. Use the inverse operation to find the missing number.

  1. Think about the total. The missing number is what is left when we take the known number away.
    300,000 - 248,000
  2. Subtract to find the missing number. Use the column method.
    300,000 - 248,000 = 52,000
  3. Check by adding. The missing number and the known number must make the total.
    248,000 + 52,000 = 300,000
  4. Write the missing number. This is the number in the box.
    52,000

Check. Check: put 52,000 into the sum and it works.

Watch out. To find a missing number in a sum, subtract. To find it in a difference, add.

Worked example 2.5.2
A town has 384,500 people. 17,250 people move away and 9,800 people move in. How many people live there now?

Method. Work out the answer in the order the story happens, one step at a time.

  1. Work out the people left after some moved away. Take away the people who moved away.
    384,500 - 17,250 = 367,250
  2. Add the people who moved in. Add the new people to the number left.
    367,250 + 9,800 = 377,050
  3. Write the answer. Check the answer makes sense in the story.
    377,050

Check. Check: the answer should fit the story; the numbers left are less than the start unless people or things came in.

Watch out. Read the whole problem first. Decide the operation for each step before you calculate.

Worked example 2.5.3
A farm grew 412,000 apples in June and 287,500 in July. The farmer sold 150,000 apples. How many apples are left?

Method. Work out the answer in the order the story happens, one step at a time.

  1. Find the total picked. Add the two months together.
    412,000 + 287,500 = 699,500
  2. Take away the apples sold. Subtract the apples that were sold.
    699,500 - 150,000 = 549,500
  3. Write the answer. Check the answer makes sense in the story.
    549,500

Check. Check: the answer should fit the story; the numbers left are less than the start unless people or things came in.

Watch out. Read the whole problem first. Decide the operation for each step before you calculate.

Watch out

Watch out. In a two-step problem, the second step uses the answer of the first step, not the original number.

Exam tip

Grown-up tip. Ask the child to say the first step, and what it tells us, before they write any numbers.

Exercise 2E  Practice: missing numbers and problems

Non-calculator
1
PSA farm grew 194,973 apples in June and 222,088 in July. The farmer sold 154,665 apples. How many apples are left?
2
F384,343 + ___ = 802,502. What is the missing number?
3
F257,682 + ___ = 495,682. What is the missing number?
4
F___ - 37,426 = 83,088. What is the missing number?
5
F11,097 + ___ = 217,543. What is the missing number?
6
F175,694 + ___ = 638,511. What is the missing number?
7
F55,917 + ___ = 504,279. What is the missing number?
8
F___ - 110,200 = 249,478. What is the missing number?
9
F102,018 + ___ = 508,306. What is the missing number?
10
F427,966 + ___ = 778,095. What is the missing number?
11
F___ - 281,988 = 340,542. What is the missing number?
12
F___ - 78,701 = 346,409. What is the missing number?
13
F255,684 + ___ = 748,123. What is the missing number?
14
PSA town has 499,278 people. 193,221 people move away and 81,406 people move in. How many people live there now?
15
F___ - 45,129 = 476,717. What is the missing number?
16
F141,505 + ___ = 486,234. What is the missing number?

Chapter summary

SkillMethod
Column additionAdd from the right; carry the ten into the next column
Column subtractionExchange 1 from the left when the top digit is smaller; across zeros, make each zero a 9
EstimatingRound each number to the nearest 10,000, then calculate
CheckingSubtract to check a sum; add back to check a difference
Missing numbersUse the inverse: subtract to find an addend, add to find a number taken away
Two-step problemsWork out the first step, then use the answer for the next

Can you…?

  • I can add two numbers with up to six digits, carrying in several columns
  • I can subtract in columns, exchanging across zeros
  • I can estimate by rounding first
  • I can check a sum by subtraction and a difference by addition
  • I can find a missing number in a sum or difference
  • I can solve two-step problems with numbers to a million

Key terms

carry
move a ten from one column to the column on its left
exchange
swap 1 from one column for 10 in the column on its right
estimate
a rough answer, found by rounding first
inverse
the operation that undoes another; subtraction undoes addition

Exercise 2Z  Check-up

Non-calculator
1
Work out 138,268 - 95,423.
2
258,175 + ___ = 604,641. What is the missing number?
3
Is 575,432 the correct answer to 442,296 + 133,146? Check it and answer Yes or No.
4
Work out 543,745 - 326,399.
5
___ - 211,998 = 338,690. What is the missing number?
6
102,640 + ___ = 409,082. What is the missing number?
7
Work out 889,951 + 50,986.
8
Work out 468,478 - 38,895.
9
Work out 94,427 + 402,923.
10
Work out 772,233 - 141,625.

Total 19 marks. Allow about 19 minutes.

Exercise 2X  Practice test questions

Non-calculator
1
FEstimate 249,766 + 351,138 by rounding each number to the nearest 10,000.[1 mark]
2
FWork out 576,455 + 373,361.[1 mark]
3
FWork out 817,441 - 119,021.[1 mark]
4
FWork out 873,435 + 106,934.[1 mark]
5
FWork out 458,296 + 124,181.[2 marks]
6
FWork out 189,824 - 45,237.[2 marks]
7
FWork out 976,424 - 330,438.[2 marks]
8
RIs 845,615 the correct answer to 633,340 + 211,275? Check it and answer Yes or No.[3 marks]
9
F460,804 + ___ = 494,697. What is the missing number?[3 marks]
10
F351,316 + ___ = 539,434. What is the missing number?[3 marks]

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